Algebraic, geometric, and stochastic aspects of genetic operators
Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.
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adaptive plan algebraic allele associated permutation basis and reflection basis set Bosworth bound is attainable bounded set bounding sphere centroid chromosome Computer coordinate value coordinate-bounded Corollary 2.2 corresponding crossover and inversion crossover operators defined Definition denote density functions distance of points easily verified Euclidean space evaluate f3Cb function composition function space game configurations game trees genetic algorithms genetic operators goal point heuristics hypersphere i=l 1 i=k+l iff i e a inner product intuitive inversion operator inversion orbit inversion pattern isomorphic itn coordinate kl k2 Lemma locus Markov Chain matrix maximal M.B.S. metric metric space minimal bounding minimal radius n-sphere centered Notation obvious penalty function plane polytope point in VSTR-space Proof quadrant random variables Remark result Section set of points strategies string Suppose Theorem 2.4 vector volume-uniform distribution VSTR space x(t+l yield